Geometry & Topology Seminar | Dominik Gutwein | The moduli space of conically singular SU(3)-instantons

Instantons over manifolds with special holonomy are a distinguished class of connections on principal bundles. In their seminal paper from 1998 Donaldson and Thomas envisioned invariants of special holonomy manifolds based on the moduli space of such instantons. However, a rigorous construction of these invariants faces formidable challenges arising from the possible non-compactness of this moduli space. One source of non-compactness comes from the formation of non-removable singularities, that is, a sequence of instantons might converge to an instanton that is singular along a subset of the underlying manifold. In this talk, I will focus on instantons over 6-manifolds with SU(3)-structures that have isolated singularities of conical type. In particular, I will discuss their moduli space, its structure, and its virtual dimension. This talk is based on joint work with Yuanqi Wang.

MC 5417